Global Attractors For Two Kinds Of Plate Equations With Memory Terms

The plate equation with memory term can be used to model flows of elastoplastic microstructures with some memory effect and it is the prototype of some important models in practical application,its research has been involved in various fields of natural science.This paper mainly studies the global attractors for two kinds of plate equations with memory terms.The details are as follows:In the first chapter,the development history of the research,the main work and results of it are introduced.In the second chapter,some concepts,lemmas and common inequalities used in this paper are listed.In the third chapter,the viscoelastic plate equation with past history and time-varying delay in the internal feedback is studied.The gradient property of the system is proved by constructing appropriate energy functional and lyapunov functional,and then a stable inequality is established by using the multiplier functional to prove the quasi-stability and asymptotic smoothness of the system,thus the existence of the global attractor of the system is obtained,and the finite fractal dimension of the attractor is proved.In the fourth chapter,the plate equations with p-Laplacian and double memory terms are studied.Based on the well-posedness of the solution,the existence of the bounded absorption set and the asymptotic compactness of the semigroup are proved by the prior estimation,the sobolev compact embedding and the common inequality,then the existence of the global attractor of the system is proved.In the fifth chapter,we make a simple summary,put forward some questions about the contents of this paper,and make the next research plan.